A Family Of Dual Explicit Algorithms With Application In Real-time Dynamic Hybrid Testing

Real-time dynamic hybrid testing (RTDHT) is a novel structural dynamic testingmethod in which the structure being emulated is split into a physical substructure and anumerical substructure. The testing is accomplished by passing data between the twosubstructures in real time. In this paper, a family of dual explicit algorithm is developedand its stability in RTDHT is analyzed. Some engineering applications of RTDHT havebeen conducted based on the proposed algorithms. The main contents include thefollowing aspects:1. A family of dual explicit algorithms is developed based on the pole mappingmethod from discrete control theory. The distinct advantage in computational efficiencyof the proposed algorithms over some traditional algorithms is demonstrated bycomparing their computational cost for solving nonlinear dynamic problem. Therelationship between the integration parameters of the proposed algorithms and theiraccuracy and stability properties are analyzed by the theoretical analysis and numericalverification. The results show that there is a contradiction between the accuracy andstability of the algorithms and they cannot achieve the highest level at the same time.The recommendations are provided to select an appropriate integration parameter inpractical computation according to the results of the numerical properties.2. A dynamic analyzing model considering the numerical integration algorithm,actuator delay and displacement compensation is established for a two degrees offreedom RTDHT system based on the discrete transfer function. The root locus methodis used to study the stability property of the proposed family of algorithms under theconditions of delay and compensation. The results show that both the delay andcompensation are key factors determining the stability limit of the algorithms inRTDHT, while the stability difference between the subfamilies under numericalcondition has little impact on the frequency limit of the structure. Thus one subfamily isvery suitable for RTDHT due to its advantage in accuracy and calculation efficiency.Some tests of a two-storey frame structure are performed to verify the stability limitfrom the root locus analysis. It can be concluded that the theoretical analysis hassufficient accuracy and can be employed to design the test model.3. A new type of feedback force measuring device is designed to measure the shear force of a non-frame structure such as a tuned liquid damper (TLD). The new deviceand the proposed algorithm are then coupled into the shaking table RTDHT system atTsinghua University to form a new testing system. The system is verified by thedynamic testing of a two-storey frame structure equipped with TLD. The result ofRTDHT agreed well with that of conventional shaking table testing, whichdemonstrated that the control efficiency of TLD can be accurately investigated by thenew RTDHT system.4. The advantage of RTDHT in adjusting the parameters of numerical substructureis used to evaluate the efficiency of TLD in reducing the seismic responses of structureswith different degrees of freedom. It is found that TLD is more efficient of high-risebuilding for energy dissipation under the same mass ratio. The performance of TLD forthe highest building mentioned above under different mass ratio, damping ratio anddifferent seismic waves have also been studied in the tests.